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1 Probing the Nucleon Structure with Azimuthal Asymmetries --cos2φ distribution & Boer-Mulders F. Lingyan Zhu University of Illinois at Urbana-Champaign FNAL E866/Nusea Collaboration Nov 21, 2006 at Jefferson Lab

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2 Sea Asymmetry from Drell-Yan Processes Towell et al., Phys.Rev. D64 (2001) 052002 Drell-Yan enables us to measured dbar/ubar asymmetry precisely.

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3 Angular Distribution in the Drell-Yan Process In the simple parton model: ( for massless quarks and measured relative to the annihilation axis) =1 and = =0

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4 Conway et al., PRD39,92(1989) First-order QCD Corrections to Drell-Yan Increase the overall cross section by a K-factor~2. The Lam-Tung relation still hold (in any reference frame for massless quarks), reflecting the spin-1/2 nature of the quarks. Lam & Tung, PRD21,2712(1980) (Analog to Callan-Gross relation in DIS) The NLO correction at O( s 2 ) to the angular distribution is small. Mirkes & Ohnemus, PRD51,,4891(1995) With QCD corrections, the calculated cross section agrees with data.

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5 Conway et al., PRD39,92(1989) E615 at Fermilab: 252 GeV π - + W Violation of the Lam-Tung Relation Also see NA10 results: 140/194 GeV π- + W, 286 GeV π- + W/d Z. Phys. C37, 545 (1988) The deviations from 1+cos 2 due to the soft-gluon resummation are less than 5%. Chiappatta & Bellac,ZPC32,521 (1986) The correction due to the intrinsic transverse momenta is estimated to be less than 0.05 Cleymans & Kuroda, PLB105,68(1981) Lam-Tung relation not affected by lowest order QCD correction even at small Q T. Boer & Wogelsang, hep-ph/0604177

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6 Conway et al., PRD39,92(1989) E615 at Fermilab: 252 GeV π - + W Angular Distribution in the W Drell-Yan Process Also see NA10 results: 140/194 GeV π- + W, 286 GeV π- + W/d Z. Phys. C31, 513 (1986); Z. Phys. C37, 545 (1988)

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7 Conway et al., PRD39,92(1989) E615 at Fermilab: 252 GeV π - + W Azimuthal cos2φ Distribution in the W Drell-Yan NA10 at CERN: 140/194/286 GeV π- + W Z. Phys. C37, 545 (1988)

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8 Possible Explanations for the cos2φ Asymmetry The high twist effect. Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994). The nuclear distortion of hadronic projectile wavefunction, typically a spin-orbit effect occurring on the nuclear surface. Bianconi & Radici, JPG31,645(2005). The spin correlation due to nontrival QCD vacuum. Brandenburg, Nachtmann & Mirkes, Z. Phy. C60,697(1993); … The hadronic effect due to non-zero Boer-Mulders function h 1 ┴. Boer, PRD60,014012(1999); …

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9 Higher Twist Effect? Higher twist effect leads to =-1 for low mass as x 1. Berger & Brodsky, PRL42, 940 (1979); Berger, ZPC4,289(1980) Higher twist effect in terms of pion bound state effect: Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994) High twist in terms of pion bound state effect is not enough.

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10 Nuclear Effect? NA10 Z. Phys. C37, 545 (1988) Open: Deuterium Solid: Tungsten Nuclear effect should not be the dominant contribution.

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11 The factorization-breaking spin correlation due to nontrivial QCD vacuum may fit the NA10 data at 194 GeV Brandenburg, Nachtmann & Mirkes, Z. Phy. C60,697(1993) The helicity flip in the instanton-induced contribution may lead to nontrivial vacuum and violation of the Lam-Tung relation. Boer,Brandenburg,Nachtmann&Utermann, EPC40,55(2005). Brandenburg,Ringwald&Uermann, hep-ph/0605234 This vacuum effect should be flavor blind. QCD Vacuum Effect 0 =0.17 m T =1.5

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12 Leading-Twist Quark Distributions Survive k ┴ integration k ┴ - dependent, T-odd k ┴ - dependent, T-even

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13 Boer-Mulders Function h 1 ┴ An spin-correlation approach in terms of h 1 ┴ can fit the NA10 data at 194 GeV. Boer, PRD60,014012(1999) On the base of quite general arguments, for |q T |<<Q(=m ), Salvo,hep-ph/0407208. 1 =0.5 m C =2.3 T =C H =1

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14 Models for Boer-Mulders Function h 1 ┴ Initial-state gluon interaction can produce nonzero h 1 ┴ for the proton in the quark-scalar diquark model. In this model, h 1 ┴ =f 1T ┴. Boer,Brodsky&Hwang, PRD67,054003(2003). Twist 2 (as well as the kinematic twist 4) contribution in a parton- spectator framework Gamberg&Goldstein, hep-ph/0506127.

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15 Pion Boer-Mulders Function Final-state interaction with one gluon exchange can produce nonzero h 1 ┴ for the pion in the quark-spectator-antiquark model with constant coupling g . Lu&Ma, PRD70,094044(2004). The quark-spectator-antiquark model with effective pion-quark- antiquark coupling as a dipole form factor Lu & Ma, hep-ph/0504184 The only model that can fit the NA10 data at different beam energy.

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16 On the basis of time reversal arguments: f 1T ┴ (x,p T 2 )=0 Collins, NPB396, 161(1993) Final-state interaction from gluon exchange between the quark and the spectator lead to nonzero Sivers function. Brodsky, Hwang & Schmidt, PLB530, 99(2002). Final-state interaction can be reproduced by a prescription of the light-cone singularities or an extra gauge link at the spatial infinity for the parton distributions. Ji & Yuan, PLB543,66(2002). Add final state interaction to the time reversal arguments: f 1T ┴ (x,p T 2 ) SIDIS =-f 1T ┴ (x,p T 2 ) DY Collins, PLB536, 43(2002) Sivers Function

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17 Models for Sivers Function f 1T ┴ Calculation fit with MIT bag model in the presence of final state interaction through one gluon exchange Yuan, PLB575, 45(2003)[hep-ph/0308157]. Calculation in a spectator model with axial-vector diquarks in the presence of gluon rescattering Bacchetta, Schaefer & Yang, PLB578,109(2004)[hep-ph/0309246] Calculation in a light-cone SU(6) quark-diquark model Lu & Ma, NPA741,200 (2004). - - These calculations are before HERMES’ transverse data.

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18 An Intuitive Explanation of Sivers Asymmetry M. Burkardt, Phys. Rev. D66(2002)114005[hep-ph/0209179]. К u =1.67 К d =-2.03 Attractive FSI f 1T ┴,q К q <0 f 1T ┴,u f 1T ┴,d <0 Attractive FSI The quark distribution in transverse polarized nucleon is deformed because the superposition of translational and orbital motion misleads the photons in the x.

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19 Sivers Function Extraction from HERMES Data Fits to the Hermes data“Prediction” of the Compass data Vogelsang and Yuan, Phys.Rev.D72(2005)054028 [hep-ph/0507266] Striking flavor dependence of the Sivers function

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20 Comparing Sivers Functions from HERMES Ref.[20] M.Anselmino et al, Phys.Rev.D72(2005)094007[hep-ph/0507181] Ref.[21] W.Vogelsang & F.Yuan, Phys.Rev.D72(2005)054028[hep-ph/0507266] Ref.[23] J.C.Collins et al, hep-ph/0510342 Satisfactory qualitative agreement between different models. M.Anselmino et al, hep-ph/0511017

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21 Comparing Boer-Mulders Functions from Models (a)MIT bag model: F. Yuan, Phys. Lett. B575,45(2003). (b)Spectator model with axial-vector diquark: Bacchetta, Schaefer & Yang, Phys. Lett. B578,109(2004). (c)Large-N C limit, P.V. Pobylitsa, hep-ph/0301236 Knowledge of the Boer-Mulders functions is very poor. Z. Lu, B.Q. Ma and I. schmidt, Phys. Lett. B639(2006)494.

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22 Unpolarized Semi-Inclusive DIS TWIST-2 Cahn Effect QED Modulation of f 1 D 1 term due to intrinsic transverse momentum. Anselmino et al., PRD71(2005) 074006 [hep-ph/0501196 ]. Add to 2(1-y+y 2 /2):

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23 Prediction of cos2φ in SIDIS Barone, Lu and Ma, Phys. Lett. B632(2006)277[hep-ph/0512145 ]. The LT curve is proportional to h 1 ┴, estimated from πN Drell-Yan. LT HT(Cahn Effect) Predictions

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24 Azimuthal Asymmetries in SIDIS from CLAS CLAS 5.7 GeV (preliminary) M.Osipenko e+Xe+X Significant cosΦ, cos2Ф observed at large P T with CLAS at 5.7 GeV V. Barone H. Avakian, Z.-E.Meziani,K.Joo and B.Seitz, JLab proposal PR12-06-112 Prediction for CLAS

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25 FNAL E866/NuSea experiment Completed Data analysis: dbar/ubar sea asymmetry Drell-Yan cross section lambda for J/Ψ production lambda for upsilon production

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26 Drell-Yan Cross Section from E866 J.C.Webb et al., hep-ex/0302019. The calculation with NLO world PDFs agrees with data.

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27 Angular Distribution of E866 p-Cu Data J/ : = 0.069±0.004±0.08 Drell-Yan (M=4~7 GeV): = 0.98±0.04 T.H. Chang et al., PRL91, 211801 (2003) (1s), (2s+3s): plotted against P T and x P. Drell-Yan: (M=8.1~8.45,11.1~15.0 GeV) =1.008±0.016±0.020 C.N. Brown et al., PRL86, 2529 (2001)

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28 Dimuon Mass Distribution Data used for cos2φ analysis: High Mass: dset7-39k (+ polarity) dset8-85k (+ polarity) dset11-25k (- polarity) Low Mass: dset5-68k (+ polarity) Towell et al., Phys.Rev. D64 (2001) 052002 Target: Proton, Deuterium

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29 Comparison of data and simulation Blue: simulation Red: data (dset8)

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30 In terms of Boer-Mulders function h 1 ┴ : ν(π - W µ + µ - X)~ valence h 1 ┴ (π) * valence h 1 ┴ (p) ν(pd µ+µ-X)~ valence h 1 ┴ (p) * sea h 1 ┴ (p) Azimuthal cos2Φ Distribution in pd Drell-Yan L.Y. Zhu,J.C. Peng, P. Reimer et al., hep-ex/0609005.

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31 Full Angular Distribution in pd Drell-Yan L.Y. Zhu,J.C. Peng, P. Reimer et al., hep-ex/0609005. No significant violation of Lam-Tung relation in pd Drell-Yan.

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32 Angular Distribution in E866 pp and pd Drell-Yan pp and pd Drell-Yan show similar angular distribution. Preliminary P T (GeV/c)

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33 Modeling Sea Boer-Mulders Functions Group led by Z. Lu, B.Q. Ma and I. Schmidt Meson-baryon fluctuation model: Predictions depend on the choice of valence Boer-Mulders functions(I,II). Group led by L. Gamburg and G. Goldstein Two possible contributions to sea from the gauge link. Preliminary p (I) d (I) d (II) p (II) Probing the sea Boer-Mulders functions may constrain the valence ones.

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34 Summary Large cos2 azimuthal asymmetry has been observed in unpolarized -induced Drell-Yan. The are a few possible explanations including the non-trivial vacuum effect and the non-zero Boer-Mulders function. The latter is related to the Sivers function. The unpolarized p-induced Drell-Yan data show only percent- level cos2φ azimuthal asymmetry. This may disfavor the flavor blind explanation such as vacuum effect. More data on unpolarized Drell-Yan will be availble from the future experiments at FNAL, RHIC with proton beam, COMPASS with pion beam and especially GSI, complementary to the SIDIS data at JLab and HERMES.

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35 Backup Slides

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36 Hadronic Effect vs. QCD Vacuum Effect D.Boer, hep-ph/0511025

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37 The Large-x Behavior of the Quark Distributions Survive k ┴ integration k ┴ -dependent, T-odd Brodsky & Yuan, hep-ph/0610236. k ┴ - dependent, T-even Sivers and Boer-Mulders functions are one power of (1-x) suppressed.

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38 Vacuum Contribution to Sivers Function f 1T ┴ Sizable instanton-induced QCD vacuum contribution to the Sivers function, adopting MIT bag model for the quark wave functions. Cherednikov, D'Alesio, Kochelev & Murgia Phys.Lett.B642:39-47,2006 [hep-ph/0606238].' thin: instanton thick: one-gluon thin: HERMES thick: total

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39 Polarized Drell-Yan Assuming u-quark dominance Burkardt Relation

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40 Unpolarized Semi-Inclusive DIS Ulrike Elschenbroich, HERMES thesis, 2006. TWIST-2 TWIST-3 Cahn Effect QED Modulation of f 1 D 1 term due to intrinsic transverse momentum. Anselmino et al., PRD71(2005) 074006 [hep-ph/0501196 ].

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41 Azimuthal moments in SIDIS (1/Q 2 )

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42 DY-experiments E615 Fermilab 80-GeV -, 252- GeV + (1989) – 36000 muon pairs NA10(1986) 194-GeV - tungsten target (145000 events) Q T -muon pair transverse momentum

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